In Ref. [1]},
Coecke argues that a process theory [2]}, [3]} is non-signalling if it satisfies a simpler condition dubbed terminality.
Terminality states that local processes on a system right before “discarding” it cannot have any observable effect (Figure REF .a). Discarding subsystems is a concept that corresponds to tracing out or coarse-graining over local information. For example, in quantum theory it is implemented by the partial trace: terminality is naturally satisfied for completely positive trace-preserving operations on the discarded systems, but does not hold for non-deterministic effects such as projections onto particular outcomes of measurements [1]}.
